scispace - formally typeset
Search or ask a question
Topic

Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, it was shown that the amplitude transformation of the wave equation is related to the Legendre transform of Ziolkowski and Deschamps, which is known as the asymptotic Fourier transform.
Abstract: Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.

95 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend Sargan's approximation theorem to include non-random exogenous variables and show that valid Edgeworth expansions can be obtained in more general models.
Abstract: THERE HAS RECENTLY BEEN A GROWING INTEREST in the use of asymptotic series expansions of the Edgeworth type to approximate finite sample distributions in econometrics. Working in the framework of a conventional simultaneous equations model, a number of authors [1, 2, 6, 7, and 13] have derived such expansions for various single-equation estimators and Sargan [10] has considered the problem of developing an expansion of the distribution of the full information maximum likelihood estimator (FIML). In addition, Sargan [11] has recently established an important general theorem on the validity of Edgeworth expansions for sample distributions of statistics which can be represented as very general functions of sample data, imposing only weak conditions on the class of functions. This result covers a wide variety of econometric estimators and test statistics. Nevertheless, work in this field to date has been based on two limiting assumptions: normally distributed structural disturbances and nonrandom exogenous variables. The latter is particularly unfortunate since models in practice usually involve lagged variables in the regressor set. On the other hand, there is no reason in principle, at least, why valid expansions cannot be obtained in more general models. The present paper, therefore, is concerned with extending Sargan's approximation theorem in [11] to include such cases. The central result of the paper is stated and proved in Section 2. In Section 3 we provide some discussion of the theorem and its conditions and attempt to relate them to the contemporaneous work of Sargan in [12].

90 citations

Journal ArticleDOI
TL;DR: In this paper, the authors define the asymptotic flatness and discuss the symmetry at null infinity in arbitrary dimensions using the Bondi coordinates, and show the symmetry and the mass loss law with the well-defined definition.
Abstract: We define the asymptotic flatness and discuss asymptotic symmetry at null infinity in arbitrary dimensions using the Bondi coordinates. To define the asymptotic flatness, we solve the Einstein equations and look at the asymptotic behavior of gravitational fields. Then we show the asymptotic symmetry and the Bondi mass loss law with the well-defined definition.

90 citations

Journal ArticleDOI
TL;DR: In this paper, a description of the asymptotic development of a family of minimum problems is proposed by a suitable iteration of Γ-limit procedures, and an example of the development of functionals related to phase transformations is also given.
Abstract: A description of the asymptotic development of a family of minimum problems is proposed by a suitable iteration of Γ-limit procedures. An example of asymptotic development for a family of functionals related to phase transformations is also given.

90 citations


Network Information
Related Topics (5)
Stochastic partial differential equation
21.1K papers, 707.2K citations
84% related
Differential equation
88K papers, 2M citations
83% related
Numerical partial differential equations
20.1K papers, 703.7K citations
82% related
Bounded function
77.2K papers, 1.3M citations
81% related
Partial differential equation
70.8K papers, 1.6M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526